Abstract
In recent years, important progress has been made in the field of
two-dimensional statistical physics. One of the most striking
achievements is the proof of the Cardy--Smirnov formula. This theorem,
together with the introduction of Schramm--Loewner Evolution and
techniques developed over the years in percolation, allow precise
descriptions of the critical and near-critical regimes of the
model. This survey aims to describe the different steps leading to the
proof that the infinite-cluster density \(\theta(p)\) for site
percolation on the triangular lattice behaves like
\((p-p_c)^{5/36+o(1)}\) as \(p\searrow p_c=1/2\).